WASHINGTON, May 13 (Reuters) - The social media giant Facebook Inc is headed toward an agreement with the U.S. government over its privacy policies and practices that would put it under 20 years of oversight, according to a source knowledgeable about the discussions.

The agreement would resolve a probe of whether the company violated a similar consent pact reached in 2011.

There had been expectations a deal was imminent after Facebook set aside $3 billion to pay what it said it expected to be a $3 billion to $5 billion penalty. But two sources said on Monday that no deal was expected this week.

One of the sources said that announcement of a settlement with the Federal Trade Commission could be a month away.

Several U.S. lawmakers have criticized aspects of a potential agreement between the FTC and Facebook that would elevate oversight of privacy policies and practices to Facebook's board of directors and require the social media company to be more aggressive in policing third-party app developers.

In a letter to the FTC, Senators Richard Blumenthal, a Democrat, and Josh Hawley, a Republican, told the agency that even a $5 billion civil penalty was too little and that top officials, potentially including founder Mark Zuckerberg, should be held personally responsible.

Facebook's 2011 settlement with the FTC also required it report to the government agency about its privacy practices for 20 years.

The FTC has been investigating allegations that Facebook inappropriately shared information belonging to 87 million users with the now-defunct British political consulting firm Cambridge Analytica. The probe has focused on whether the sharing of data and other disputes violated the 2011 consent agreement.

The lapse, as well as anger over hate speech and misinformation on its platform, has prompted calls from people ranging from progressive presidential candidate Senator Elizabeth Warren to a Facebook co-founder, Chris Hughes, for the government to force the social media giant to sell Instagram, which it bought in 2012, and WhatsApp, purchased in 2014.

Despite its scandals, the company's core business has proven resilient as Facebook blew past earnings estimates in the past two quarters. (Reporting by Diane Bartz; Editing by Dan Grebler)